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Why difference between area and perimeter is always 4 if one side of a rectangle is 2?
Wiki User
∙ 11y ago
We can answer this by analyzing the algebraic formulas for perimeter and area of any given rectangle.
Assuming the length of the rectangle is 2 and the width is x we have the following diagram (ignore the periods they are just spacers since Answers.com won't let me format a diagram properly):
... _____x______
...|......................|
2 |......................| 2
...|___________|
............ x
Area is found by multiplying the length times width, so we get: A = 2x
The perimeter is found by adding all the sides, thus: P = x + x + 2 + 2
which simplifies to the following: P = 2x + 4
Here we can see that since A = 2x, and P = 2x + 4, that by using substitution (plugging in A where 2x is in the P formula) we find the formula for perimeter is the Area plus 4:
P = A + 4
So this shows that for any rectangle with a side length of 2 and another of any length x, the perimeter will always be 4 more than the area.
Wiki User
∙ 11y ago
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In general describe the rectangle that has the least area for a fixed perimeter?
For a fixed perimeter, the area will always be the same, regardless of how you describe the rectangle.
A rectangle had an area of 24ft2 what is the length and width of the rectangle with the greatest perimeter?
The rectangle with the smallest perimeter for a given area is the square. The rectangle with the greatestperimeter for a given area can't be specified. The longer and skinnier you make the rectangle, the greater its perimeter will become. No matter how great a perimeter you use to enclose 24 ft2, I can always specify a longer perimeter. Let me point you in that direction with a few examples: 6 ft x 4 ft = 24 ft2, perimeter = 20 ft 8 ft x 3 ft = 24 ft2, perimeter = 22 ft 12 ft x 2 ft = 24 ft2, perimeter = 28 ft 24 ft x 1 ft = 24 ft2, perimeter = 50 ft 48 ft x 6 inches = 24 ft2, perimeter = 97 ft 96 ft x 3 inches = 24 ft2, perimeter = 192.5 ft 288 ft x 1 inch = 24 ft2, perimeter = 576ft 2inches No matter how great a perimeter you find to enclose 24 ft2, I can always specify a rectangle with the same area and a longer perimeter.
Does a rectangle have congruent lines?
Rectangles do not have congruent lines. A square can always be called a rectangle. But a rectangle can't always be a square.
How do you prove that a parallelogram is a rectangle?
a rectangle has four right angles and opposite sides are all the same length This means that a parallelogram is not always a rectangle, but a rectangle is always a parallelogram, by definition.
Is the difference between two integers always smaller than either on of the numbers in the difference?
Yes
Is The area of a rectangle always greater than the perimeter?
To answer this simply try a few out for yourself. In a 2x1 cm rectangle, the area is 2 cm squared and the perimeter is 6 cm In a 12x10 rectangle, the area is 120 cm squared and the perimeter is 44 cm. In some cases, the perimeter is larger and in others it is smaller. To answer your question, no, the perimeter of a rectangle is NOT always greater than its area.
In general describe the rectangle that has the least area for a fixed perimeter?
For a fixed perimeter, the area will always be the same, regardless of how you describe the rectangle.
Why is the perimeter of a rectangle always even?
The perimeter of a rectangle is always even because the perimeter is twice the length plus twice the width. Whenever you multiply a number by 2, the product is even. When you add two even numbers the sum is even.
Does changing the area always change the perimeter?
No. A rectangle of 1 x 3 has the same perimeter as a rectangle of 2 x 2, but the areas are different.
How does increasing the dimensions of a rectangle impact the perimeter?
If you increase the rectangle's length by a value, its perimeter increases by twice that value. If you increase the rectangle's width by a value, its perimeter increases by twice that value. (A rectangle is defined by its length and width, and opposite sides of a rectangle are the same length. The lines always meet at their endpoints at 90° angles.)
Can a rectangle have the same perimeter but different area explain?
No, any shape with four sides and same perimeter will always be a square.
Are two rectangles with the same perimeter always congruent to each other?
no because one rectangle may be 3x4 which the perimeter is 14 and one rectangle may be 5x2 which as well equals 14
If two rectangle have the same area must they have the same perimeter?
Not always because a 2 by 12 rectangle will have the same area as a 4 by 6 rectangle but they both will have different perimeters.
Can you give a counter example to show that a rectangle does not always have a perimeter which is not an even number?
A rectangle whose opposite sides are 4 cm and 2.5 cm. Its perimeter is 2*(4 + 2.5) = 2*6.5) = 13 cm.
A rectangle had an area of 24ft2 what is the length and width of the rectangle with the greatest perimeter?
The rectangle with the smallest perimeter for a given area is the square. The rectangle with the greatestperimeter for a given area can't be specified. The longer and skinnier you make the rectangle, the greater its perimeter will become. No matter how great a perimeter you use to enclose 24 ft2, I can always specify a longer perimeter. Let me point you in that direction with a few examples: 6 ft x 4 ft = 24 ft2, perimeter = 20 ft 8 ft x 3 ft = 24 ft2, perimeter = 22 ft 12 ft x 2 ft = 24 ft2, perimeter = 28 ft 24 ft x 1 ft = 24 ft2, perimeter = 50 ft 48 ft x 6 inches = 24 ft2, perimeter = 97 ft 96 ft x 3 inches = 24 ft2, perimeter = 192.5 ft 288 ft x 1 inch = 24 ft2, perimeter = 576ft 2inches No matter how great a perimeter you find to enclose 24 ft2, I can always specify a rectangle with the same area and a longer perimeter.
What is the maximum area of a rectangle with a perimeter of 130?
130/4 (4 sides to a rectangle)= 32.5 32.5*32.5=1065.25 square meters (because the largest area of a rectangle is always a ^ ^ square). length width
How does the length and width of a rectangle relate to the perimeter?
If you add the length and width together, it will always be half of the perimeter. In terms of an equation, it would look like so: Perimeter = (2 x Length) + (2 x Width)
